Leading members of the US Republican Party have joined calls for a wide investigation into the former national security adviser’s links with Russia.
Michael Flynn quit on Monday over claims he discussed US sanctions with Russia before Donald Trump took office.
On Tuesday, a White House spokesman said Mr Trump knew weeks ago there were problems with the Russia phone calls.
But calls for an independent investigation have encountered a cold response from some senior Republicans.
The development came as the New York Times reported that phone records and intercepted calls show members of Mr Trump’s presidential campaign, as well as other Trump associates, “had repeated contacts with senior Russian intelligence officials in the year before the election”.
However, officials spoken to by the newspaper said they had not yet seen evidence that the Trump campaign colluded with Russia on the hacking of the Democratic National Committee or to influence the election.
As well as an FBI investigation, both the Senate and House intelligence committees are already examining Russian involvement in the election. It is not yet clear whether the latest claims will be included in their scope.
Why Mr Flynn resigned
He stood down over allegations he discussed US sanctions with a Russian envoy in December, before Mr Trump took office.
The conversations took place about the time that then-President Barack Obama was imposing retaliatory measures on Russia following reports it attempted to sway the US election in Mr Trump’s favour.
Mr Flynn could have broken a law – known as the Logan Act – by conducting US diplomacy as a private citizen, before he was appointed as national security adviser.
The retired army lieutenant-general initially denied having discussed sanctions with Ambassador Sergei Kislyak. Vice-President Mike Pence publicly denied the allegations on his behalf.
The White House admitted it had been warned about the contacts on 26 January but President Trump initially concluded Mr Flynn had not broken any law.
White House lawyers then conducted a review and questioned Mr Flynn before reaching the same conclusion as Mr Trump, White House spokesman Sean Spicer said, but the trust had gone.
“In the end, it was misleading the vice-president that made the situation unsustainable,” White House Counsellor Kellyanne Conway said on Tuesday.
Mr Flynn was also reportedly questioned by FBI agents in his first days as national security adviser, according to US media.
What Mr Flynn says
In an interview conducted with the conservative website The Daily Caller on Monday, but published only on Tuesday, Mr Flynn said he “crossed no lines” in his conversation with the ambassador.
He said he discussed the expulsion of 35 Russian diplomats over alleged hacking ahead of the election, but “it wasn’t about sanctions”.
He said he was concerned that the apparently classified information had been leaked. “In some of these cases, you’re talking about stuff that’s taken off of a classified system and given to a reporter,” he said. “That’s a crime.”
However, in his resignation letter, Mr Flynn said “the fast pace of events” during the presidential transition meant that he had “inadvertently briefed the vice-president elect and others with incomplete information regarding my phone calls with the Russian ambassador”.
In his first public comments about the controversy, President Trump tweeted on Tuesday: “The real story here is why are there so many illegal leaks coming out of Washington? Will these leaks be happening as I deal on N Korea etc?”
US House Intelligence Committee Chairman Devin Nunes told reporters on Tuesday he wanted to examine the leaks, and said the FBI should explain why Mr Flynn’s conversation had been recorded.
But the Senate’s second-ranking Republican,John Cornyn, and other Republican senators have called for an investigation into Mr Trump’s connections with Russian officials.
Republican John McCain, Chairman of the Senate Armed Services Committee, said Mr Flynn’s resignation was a “troubling indication of the dysfunction of the current national security apparatus”, which raised questions about Mr Trump’s intentions towards Russia.
Meanwhile, the Senate’s most senior Republican, Mitch McConnell, said the intelligence committee was already looking into Russian influence on the election, indicating there was no need for a new investigative panel.
Kremlin spokesman Dmitry Peskov said Russia would not be commenting on the resignation.
“This is the internal affair of the Americans, the internal affair of the Trump administration,” he added. “It’s nothing to do with us.”
What will America’s allies think? – by BBC diplomatic correspondent Jonathan Marcus
Gen Flynn’s resignation comes just as senior US officials are mounting a major effort to reassure uncertain allies in Europe about the Trump administration’s intentions.
The new US Defence Secretary General James Mattis, Secretary of State Rex Tillerson and Vice-President Mike Pence are all in Europe over the coming days. Gen Mattis is in the vanguard – he meets his Nato counterparts in Brussels on Wednesday.
There will be few tears shed within the alliance over Gen Flynn. His was widely seen as a bizarre and destabilising appointment.
But his demise and the rumbling row over team Trump’s contacts with Russia continues to cause unease at Nato where many governments wonder at the Trump administration’s resolve in standing up to what they see as a new assertiveness from Moscow.
Many key US officials are still to be appointed and the continuing chaos at the heart of the Trump administration is a cause for concern among Nato countries whatever reassurance the heavyweight US diplomatic trio may bring.
Democrat Adam Schiff, a member of the House Permanent Select Committee on Intelligence, has said Mr Flynn’s departure will not end questions about contacts between Trump’s campaign and Russia. But there are various ways that these questions could be answered.
Two Democratic members of the House of Representatives have demanded a classified briefing to Congress on Michael Flynn by the justice department and FBI.
Several House Democrats had already called on Oversight Committee Chairman Jason Chaffetz to launch an investigation into Mr Flynn’s ties to Russia.